A pulsed beam (PB) expansion algorithm for time-dependant radiation from a point source is presented. The source field is expanded in terms of a lattice of PB propagators emerging from the source in all directions. The optimal expansion parameters, namely the beam collimation and the spectral discretization and truncation, are determined as functions of the observation range and the pulse length. In the basic scheme, the PB propagators are expressed in terms of the analytic signal extension of the source signal which needs to be calculated a-priori. We also present a modified scheme that may accommodate arbitrary source signals specified by a series of time-samples.